Chapter 30 The Nature of the Atom
Chapter 30
THE NATURE OF THE ATOM
PREVIEW
The atom is the smallest particle of an element that can be identified with that element.
The atom consists of a nucleus surrounded by electrons which are in quantized, or
discrete, energy levels. An electron can only change energy levels when it absorbs or
emits energy. The energy emitted as a result of a downward energy level transition is
typically in the form of a photon, the smallest particle of light, and the energy of the
emitted photon is equal to the difference between the initial and final energy of the
electron.
The content contained in sections 2, 3, 4, and 11 of chapter 30 of the textbook is included
on the AP Physics B exam.
QUICK REFERENCE
Important Terms
atom
the smallest particle of an element that can be identified with that element; the
atom consists of protons and neutrons in the nucleus, and electrons in orbitals
around the nucleus.
electron
the smallest negatively charged particle; electrons orbit the nucleus of the atom
energy level
amount of energy an electron has while in a particular orbit around the
nucleus of an atom
excited state
the energy level of an electron in an atom after it has absorbed energy
ground state
the lowest energy level of an electron in an atom
ionization energy
the energy needed to completely remove an electron from its orbital in an atom
line spectrum
discrete lines which are emitted by a cool excited gas
principal quantum number
an integer number n which determines the total energy of an atom
quantum model of the atom
atomic model in which only the probability of locating an electron is known
x-rays
high frequency and energy electromagnetic waves which are produced when highenergy electrons strike a metal target in an evacuated tube
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Chapter 30 The Nature of the Atom
Equations and Symbols
E = hf =
where
hc
λ
E = energy of a photon
c = speed of light = 3 x 108 m/s
f = frequency of light
λ = wavelength of light
Ef – Ei = difference between a final
energy level of an electron in an
atom and its initial energy
c = fλ
E photon = E f − Ei
Ten Homework Problems
Chapter 30 Problems 8, 9, 11, 12, 39, 40, 41, 45, 52, 53
DISCUSSION OF SELECTED SECTIONS
30.2 Line Spectra
The ancient Greeks were the first to document the concept of the atom. They believed
that all matter is made up of tiny indivisible particles. In fact, the word atom comes from
the Greek word atomos, meaning “uncuttable”. But a working model of the atom didn’t
begin to take shape until J.J. Thomson’s discovery of the electron in 1897. He found that
electrons are tiny negatively charged particles and that all atoms contain electrons. He
also recognized that atoms are naturally neutral, containing equal amounts of positive and
negative charge, although he was not correct in his theory of how the charge was
arranged.
You may remember studying Thomson’s “plum-pudding” model of the atom, with
electrons floating around in positive fluid. A significant improvement on this model of
the atom was made by Ernest Rutherford around 1911, when he decided to shoot alpha
particles (helium nuclei) at very thin gold foil to probe the inner structure of the atom. He
discovered that the atom has a dense, positively charged nucleus with electrons orbiting
around it.
Nucleus
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electron in
orbit
Chapter 30 The Nature of the Atom
In 1913, Niels Bohr made an important improvement to the Rutherford model of the
atom. He observed that excited hydrogen gas gave off a spectrum of colors when viewed
through a spectrosope. But the spectrum was not continuous, that is, the colors were
bright, sharp lines which were separate from each other. It had long been known that
every low pressure, excited gas emitted its own special spectrum in this way, but Bohr
was the first to associate the bright-line spectra of these gases, particularly hydrogen,
with a model of the atom. Section 30.2 in your textbook has excellent photographs of
continuous and bright-line spectra.
Bohr proposed that the electrons orbiting the nucleus of an atom do not radiate energy in
the form of light while they are in a particular orbit, but only when they change orbits.
Furthermore, an electron cannot orbit at just any radius around the nucleus, but only
certain selected (quantized) orbits.
30.3 The Bohr Model of the Hydrogen Atom
The two postulates of the Bohr model of the atom are summarized below:
1. Electrons orbiting the nucleus of an atom can only orbit in certain quantized orbits,
and no others. These orbits from the nucleus outward are designated n =1, 2, 3…, and
the electron has energy in each of these orbits E1, E2, E3, and so on. The energies of
electrons are typically measured in electron-volts (eV). The lowest energy (in the
orbit nearest the nucleus) is called the ground state energy E1. (Fig. A)
n=2
n=1
E2
E1
E3
E3
E2
E2
photon
photon E = E2-E1
E1
Fig. A
Fig. B
E1
Fig. C
2. Electrons can change orbits when they absorb or emit energy.
(a) When an electron absorbs exactly enough energy to reach a higher energy level, it
jumps up to that level. If the energy offered to the electron is not exactly enough
to raise it to a higher level, the electron will ignore the energy and let it pass.
(Fig. B)
(b) When an electron is in a higher energy level, it can jump down to a lower energy
level by releasing energy in the form of a photon of light. The energy of the
emitted photon is exactly equal to the difference between the energy levels the
electron moves between.
(Fig. C)
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Chapter 30 The Nature of the Atom
Example 1
Consider the energy level diagram for a particular atom shown below:
Energy above
ground state
E4 = 7 eV
E3 = 6 eV
E2 = 4 eV
E1 = 0
An electron begins in the ground state of this atom.
(a) How much energy must be absorbed by this electron to reach the 4th energy level?
(b) How many possible photons can be emitted from this atom if the electron starts in the
4th energy level? Sketch the possible transitions on the diagram above using arrows to
indicate a transition between levels.
(c) The electron drops from E4 to E2 and emits a photon, then drops from E2 to E1 and
emits a second photon.
i. Calculate the frequency and wavelength of the photon emitted when the electron
drops from E4 to E2.
ii. Calculate the frequency and wavelength of the photon emitted when the electron
drops from E2 to E1.
(d) Are either, both, or neither of the photons emitted in part (c) above in the visible
range? How can you tell?
Solution
(a) E = E4 – E1 = 7 eV – 0 eV = 7 eV
E4 = 7 eV
(b) Six possible transitions
E3 = 6 eV
E2 = 4 eV
E1 = 0
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Chapter 30 The Nature of the Atom
(c) i. E42 = E4 – E2 = 7 eV – 4 eV = 3 eV
3 eV
E
f = =
= 7.2 x1014 Hz
−15
h 4.14 x10 eV / Hz
c
3 x10 8 m / s
λ= =
= 4.1x10 −7 m
14
f 7.2 x10 Hz
ii. E21 = E2 – E1 = 4 eV – 0 eV = 4 eV
4 eV
E
f = =
= 9.7 x1014 Hz
h 4.14 x10 −15 eV / Hz
c
3 x10 8 m / s
λ= =
= 3.1x10 −7 m
14
f 9.7 x10 Hz
(d) The range of visible wavelengths is about 4 x 10-7 m to 7 x 10-7 m. The photon
emitted in the transition from E4 to E2 is in this visible range, but the photon emitted in
the transition from E2 to E1 is not in this range.
CHAPTER 30 REVIEW QUESTIONS
For each of the multiple-choice questions below, choose the best answer.
1. An emission spectrum is produced
when
(A) electrons in an excited gas jump up
to a higher energy level and release
photons.
(B) electrons in an excited gas jump
down to a lower energy level and
release photons.
(C) electrons are released from the outer
orbitals of an excited gas.
(D) an unstable nucleus releases energy.
(E) light is shined on a metal surface and
electrons are released.
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Chapter 30 The Nature of the Atom
Energy above
ground state
E5 = -0.54 eV
E5 = 5 eV
E4 = -0.85 eV
E4 = 4 eV
E3 = -1.5 eV
E3 = 3 eV
E2 = -3.4 eV
E2 = 2 eV
E1 = -13.6 eV
E1 = 0
3. Consider the electron energy level
diagram for hydrogen shown. An
electron in the ground state of a
hydrogen atom has an energy of
- 13.6 eV. Which of the following
energies is NOT a possible energy
for a photon emitted from hydrogen?
(A) 1.9 eV
(B) 13.6 eV
(C) 0.65 eV
(D) 11.1 eV
(E) 10.2 eV
2. Consider the electron energy level
diagram for a particular atom shown
above. An electron is in the ground state
energy level. If a photon of energy 6 eV
is given to the electron, which of the
following will occur?
(A) The electron will ignore the photon
since the photon’s energy does not
match the energy levels.
(B) The electron will absorb the photon,
jump up to the 5-eV level shown,
and convert the remainder of the
photon’s energy into kinetic energy,
but will stay in the 5-eV energy
level.
(C) The electron will absorb the photon,
jump out of the atom completely,
and convert the remainder of the
photon’s energy into kinetic energy.
(D) The electron will absorb the photon,
jump up to the 5-eV level, then back
down to the 4 eV level.
(E) The electron will jump up to the 3eV level, then immediately back
down to the ground state.
4. The reason why electrons can only
orbit at certain circumferences is
(A) some electrons are larger than others
(B) the energy of electrons gets smaller
as the circumference gets larger
(C) electrons do not radiate energy when
they are in a particular orbit
(D) the atom is mostly empty space
(E) a whole number of de Broglie
wavelengths of the electron must fit
into the orbit.
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Chapter 30 The Nature of the Atom
Free Response Question
Directions: Show all work in working the following question. The question is worth 10
points, and the suggested time for answering the question is about 10 minutes. The parts
within a question may not have equal weight.
1. (10 points)
E=0
E4 = - 0.85 eV
E3 = -1.51 eV
E2 = -3.4 eV
E1 = -13.6 eV
The energy level diagram for hydrogen is shown above. A free electron comes close
enough to the hydrogen atom that it is captured and makes a transition to the third energy
level of the atom. Then the electron makes a transition to the first energy level.
(a) Sketch arrows on the diagram above representing the two transitions made by the
electron.
(b) Calculate the wavelength of the photon emitted as the electron makes the transition to
the third energy level.
While the electron is in the ground state it absorbs a 17-eV photon.
(c) Briefly describe what happens to the electron as a result of absorbing the 17-eV
photon.
(d) Calculate the de Broglie wavelength of the electron after absorbing the 17-eV photon.
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Chapter 30 The Nature of the Atom
ANSWERS AND EXPLANATIONS TO CHAPTER 30 REVIEW QUESTIONS
Multiple Choice
1. B
When electrons jump back to lower energy levels, they emit energy as photons.
2. C
When an electron absorbs enough energy to completely escape the atom we say that the
atom is ionized, and the energy remaining, in this case 1 eV, is converted to kinetic
energy.
3. D
An electron emits a photon of energy which corresponds exactly to the difference in two
energy levels, and 11.1 eV does not correspond to any energy differences in the hydrogen
atom.
4. E
If a whole number of electron wavelengths does not fit into a particular circumference,
the electron wave would destructively interfere and could not exist in that orbit.
Free Response Question Solution
E=0
(a) 2 points
photon
(b) 3 points
hc
hc
=
λ=
E E3 − 0
E4 = - 0.85 eV
E3 = -1.51 eV
E2 = -3.4 eV
1240 eV nm
= 821.2nm
1.51 eV
(c) 2 points
It takes 13.6 eV to release the
electron from the ground state,
and the remaining energy of 3.4 eV
is the kinetic energy of the freed electron.
λ=
photon
E1 = -13.6 eV
(d) 3 points
The speed of the ejected electron is
v=
λ=
2 KE
=
m
(
)
2(3eV ) 1.6 x10 −19 J / eV
= 1.0 x10 6 m / s
9.1x10 −31 kg
h
6.6 x10 −34 J / Hz
=
= 7.1x10 −10 m
− 31
6
mv 9.1x10 kg 1.0 x10 m / s
(
)(
)
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